Change the following limit of a Riemann sum for $A(f,-2 ≤ x ≤ 1)$ into an integral expression. Then, evaluate with your graphing calculator.

$\lim\limits_ { n \rightarrow \infty }\displaystyle \sum _ { i = 1 } ^ { n } \Delta x _ { i } ( ( x _ { i } ) ^ { 1 / 3 } - 4 )$